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*DECK TRICHH
SUBROUTINE TRICHH(IMPX,MAXKN,NBLOS,LXH,LZ,IELEM,ISPLH,L4,LL4F,
1 LL4W,LL4X,LL4Y,LL4Z,SIDE,ZZ,FRZ,IPERT,KN,V,H,MUW,MUX,MUY,MUZ,
2 IPBBW,IPBBX,IPBBY,IPBBZ,BBW,BBX,BBY,BBZ,CTRAN)
*
*-----------------------------------------------------------------------
*
*Purpose:
* Thomas-Raviart-Schneider (dual) finite element unknown numbering for
* ADI solution in a 3D hexagonal domain. Compute the storage info for
* ADI matrices in compressed diagonal storage mode. Compute the ADI
* permutation vectors. Compute the group-independent WB, XB, YB and ZB
* matrices.
*
*Copyright:
* Copyright (C) 2006 Ecole Polytechnique de Montreal
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version
*
*Author(s): A. Hebert
*
*Parameters: input
* IMPX print parameter.
* MAXKN number of components in KN.
* NBLOS number of lozenges per direction in 3D with mesh-splitting.
* LXH number of hexagons in a plane.
* LZ number of elements along the Z axis.
* IELEM degree of the Lagrangian finite elements: =1 (linear);
* =2 (parabolic); =3 (cubic).
* ISPLH mesh-splitting in 3*ISPLH**2 lozenges per hexagon.
* L4 total number of unknown (variational coefficients) per
* energy group (order of system matrices).
* LL4F exact number of flux unknowns.
* LL4W exact number of W-directed current unknowns.
* LL4X exact number of X-directed current unknowns.
* LL4Y exact number of Y-directed current unknowns.
* LL4Z exact number of Z-directed current unknowns.
* SIDE side of an hexagon.
* ZZ Z-directed mesh spacings.
* FRZ volume fractions for the axial SYME boundary condition.
* IPERT mixture permutation index.
* KN ADI permutation indices for the volumes and currents.
* V nodal coupling matrix matrix.
* H Piolat (hexagonal) coupling matrix.
*
*Parameters: output
* MUW W-directed compressed diagonal mode indices.
* MUX X-directed compressed diagonal mode indices.
* MUY Y-directed compressed diagonal mode indices.
* MUZ Z-directed compressed diagonal mode indices.
* IPBBW W-directed perdue storage indices.
* IPBBX X-directed perdue storage indices.
* IPBBY Y-directed perdue storage indices.
* IPBBZ Z-directed perdue storage indices.
* BBW W-directed flux-current matrices.
* BBX X-directed flux-current matrices.
* BBY Y-directed flux-current matrices.
* BBZ Z-directed flux-current matrices.
* CTRAN tranverse coupling Piolat unit matrix.
*
*-----------------------------------------------------------------------
*
*----
* SUBROUTINE ARGUMENTS
*----
INTEGER IMPX,MAXKN,NBLOS,LXH,LZ,IELEM,ISPLH,L4,IPERT(NBLOS),
1 KN(NBLOS,MAXKN/NBLOS),LL4F,LL4W,LL4X,LL4Y,LL4Z,MUW(L4),
2 MUX(L4),MUY(L4),MUZ(L4),IPBBW(2*IELEM,LL4W),IPBBX(2*IELEM,LL4X),
3 IPBBY(2*IELEM,LL4Y),IPBBZ(2*IELEM,LL4Z)
REAL SIDE,ZZ(3,NBLOS),FRZ(NBLOS),V(IELEM+1,IELEM),
1 H(IELEM+1,IELEM),BBW(2*IELEM,LL4W),BBX(2*IELEM,LL4X),
2 BBY(2*IELEM,LL4Y),BBZ(2*IELEM,LL4Z)
DOUBLE PRECISION CTRAN((IELEM+1)*IELEM,(IELEM+1)*IELEM)
*----
* LOCAL VARIABLES
*----
DOUBLE PRECISION TTTT,DENOM,VOL0
*
NELEH=(IELEM+1)*IELEM**2
NELEZ=6*IELEM**2
NBC=INT((SQRT(REAL((4*LXH-1)/3))+1.)/2.)
IF(LL4F.GT.3*NBLOS*IELEM**3) CALL XABORT('TRICHH: BUG1.')
IF(LL4W.GT.(2*NBLOS*IELEM+(2*NBC-1)*ISPLH*LZ)*IELEM**2)
1 CALL XABORT('TRICHH: BUG2.')
*----
* COMPUTE THE TRANVERSE COUPLING PIOLAT UNIT MATRIX
*----
CTRAN(:(IELEM+1)*IELEM,:(IELEM+1)*IELEM)=0.0D0
CNORM=SIDE*SIDE/SQRT(3.)
I=0
DO 22 JS=1,IELEM
DO 21 JT=1,IELEM+1
J=0
I=I+1
SSS=1.0
DO 20 IT=1,IELEM
DO 10 IS=1,IELEM+1
J=J+1
CTRAN(I,J)=SSS*CNORM*H(IS,JS)*H(JT,IT)
10 CONTINUE
SSS=-SSS
20 CONTINUE
21 CONTINUE
22 CONTINUE
IF(IMPX.GT.1) THEN
WRITE(6,*) 'TRICHH: MATRIX CTRAN'
DO 30 I=1,(IELEM+1)*IELEM
WRITE(6,'(10(1X,1P,E12.4))') (CTRAN(I,J),J=1,(IELEM+1)*IELEM)
30 CONTINUE
WRITE(6,*) ' '
ENDIF
*----
* COMPUTE THE W-, X- ,Y- AND Z-ORIENTED SYSTEM BANDWIDTH VECTORS
*----
MUW(:L4)=1
MUX(:L4)=1
MUY(:L4)=1
MUZ(:L4)=1
IPBBW(:2*IELEM,:LL4W)=0
IPBBX(:2*IELEM,:LL4X)=0
IPBBY(:2*IELEM,:LL4Y)=0
IPBBZ(:2*IELEM,:LL4Z)=0
NUM=0
DO 80 KEL=1,NBLOS
IF(IPERT(KEL).EQ.0) GO TO 80
NUM=NUM+1
DO 64 K5=0,1 ! TWO LOZENGES PER HEXAGON
DO 63 K4=0,IELEM-1
DO 62 K3=0,IELEM-1
DO 61 K2=1,IELEM+1
KNW1=KN(NUM,3+K5*NELEH+(K4*IELEM+K3)*(IELEM+1)+K2)
KNX1=KN(NUM,3+(K5+2)*NELEH+(K4*IELEM+K3)*(IELEM+1)+K2)
KNY1=KN(NUM,3+(K5+4)*NELEH+(K4*IELEM+K3)*(IELEM+1)+K2)
INW1=ABS(KNW1)
INX1=ABS(KNX1)-LL4W
INY1=ABS(KNY1)-LL4W-LL4X
DO 40 K1=1,IELEM+1
KNW2=KN(NUM,3+K5*NELEH+(K4*IELEM+K3)*(IELEM+1)+K1)
KNX2=KN(NUM,3+(K5+2)*NELEH+(K4*IELEM+K3)*(IELEM+1)+K1)
KNY2=KN(NUM,3+(K5+4)*NELEH+(K4*IELEM+K3)*(IELEM+1)+K1)
INW2=ABS(KNW2)
INX2=ABS(KNX2)-LL4W
INY2=ABS(KNY2)-LL4W-LL4X
IF((KNW2.NE.0).AND.(KNW1.NE.0)) THEN
MUW(INW1)=MAX(MUW(INW1),INW1-INW2+1)
MUW(INW2)=MAX(MUW(INW2),INW2-INW1+1)
ENDIF
IF((KNX2.NE.0).AND.(KNX1.NE.0)) THEN
MUX(INX1)=MAX(MUX(INX1),INX1-INX2+1)
MUX(INX2)=MAX(MUX(INX2),INX2-INX1+1)
ENDIF
IF((KNY2.NE.0).AND.(KNY1.NE.0)) THEN
MUY(INY1)=MAX(MUY(INY1),INY1-INY2+1)
MUY(INY2)=MAX(MUY(INY2),INY2-INY1+1)
ENDIF
40 CONTINUE
DO 60 K1=0,IELEM-1
IF(V(K2,K1+1).EQ.0.0) GO TO 60
IF(K5.EQ.0) THEN
JND1=(NUM-1)*IELEM**3+K4*IELEM**2+K3*IELEM+K1+1
JND2=(KN(NUM,1)-1)*IELEM**3+K4*IELEM**2+K3*IELEM+K1+1
JND3=(KN(NUM,2)-1)*IELEM**3+K4*IELEM**2+K3*IELEM+K1+1
ELSE
JND1=(KN(NUM,1)-1)*IELEM**3+K4*IELEM**2+K1*IELEM+K3+1
JND2=(KN(NUM,2)-1)*IELEM**3+K4*IELEM**2+K1*IELEM+K3+1
JND3=(KN(NUM,3)-1)*IELEM**3+K4*IELEM**2+K1*IELEM+K3+1
ENDIF
IF(KNW1.NE.0) CALL TRINDX(JND1,IPBBW(1,INW1),2*IELEM)
IF(KNX1.NE.0) CALL TRINDX(JND2,IPBBX(1,INX1),2*IELEM)
IF(KNY1.NE.0) CALL TRINDX(JND3,IPBBY(1,INY1),2*IELEM)
60 CONTINUE
61 CONTINUE
62 CONTINUE
63 CONTINUE
64 CONTINUE
DO 73 K5=0,2 ! THREE LOZENGES PER HEXAGON
DO 72 K2=0,IELEM-1
DO 71 K1=0,IELEM-1
KNZ1=KN(NUM,3+6*NELEH+2*K5*IELEM**2+K2*IELEM+K1+1)
KNZ2=KN(NUM,3+6*NELEH+(2*K5+1)*IELEM**2+K2*IELEM+K1+1)
INZ1=ABS(KNZ1)-LL4W-LL4X-LL4Y
INZ2=ABS(KNZ2)-LL4W-LL4X-LL4Y
IF((KNZ1.NE.0).AND.(KNZ2.NE.0)) THEN
MUZ(INZ2)=MAX(MUZ(INZ2),INZ2-INZ1+1)
MUZ(INZ1)=MAX(MUZ(INZ1),INZ1-INZ2+1)
ENDIF
DO 70 K3=0,IELEM-1
IF(K5.EQ.0) THEN
JND1=(NUM-1)*IELEM**3+K3*IELEM**2+K2*IELEM+K1+1
ELSE
JND1=(KN(NUM,K5)-1)*IELEM**3+K3*IELEM**2+K2*IELEM+K1+1
ENDIF
IF(KNZ1.NE.0) CALL TRINDX(JND1,IPBBZ(1,INZ1),2*IELEM)
IF(KNZ2.NE.0) CALL TRINDX(JND1,IPBBZ(1,INZ2),2*IELEM)
70 CONTINUE
71 CONTINUE
72 CONTINUE
73 CONTINUE
80 CONTINUE
*
MUWMAX=0
IIMAXW=0
DO 90 I=1,LL4W
MUWMAX=MAX(MUWMAX,MUW(I))
IIMAXW=IIMAXW+MUW(I)
MUW(I)=IIMAXW
90 CONTINUE
MUXMAX=0
IIMAXX=0
DO 100 I=1,LL4X
MUXMAX=MAX(MUXMAX,MUX(I))
IIMAXX=IIMAXX+MUX(I)
MUX(I)=IIMAXX
100 CONTINUE
MUYMAX=0
IIMAXY=0
DO 110 I=1,LL4Y
MUYMAX=MAX(MUYMAX,MUY(I))
IIMAXY=IIMAXY+MUY(I)
MUY(I)=IIMAXY
110 CONTINUE
MUZMAX=0
IIMAXZ=0
DO 120 I=1,LL4Z
MUZMAX=MAX(MUZMAX,MUZ(I))
IIMAXZ=IIMAXZ+MUZ(I)
MUZ(I)=IIMAXZ
120 CONTINUE
IF(IMPX.GT.0) THEN
WRITE (6,600) MUWMAX,MUXMAX,MUYMAX,MUZMAX
WRITE (6,610) IIMAXW,IIMAXX,IIMAXY,IIMAXZ
ENDIF
*----
* COMPUTE THE FLUX-CURRENT COUPLING MATRICES WB, XB, YB AND ZB.
*----
BBW(:2*IELEM,:LL4W)=0.0
BBX(:2*IELEM,:LL4X)=0.0
BBY(:2*IELEM,:LL4Y)=0.0
BBZ(:2*IELEM,:LL4Z)=0.0
TTTT=0.5D0*SQRT(3.D00)*SIDE*SIDE
DENOM=0.5D0*SQRT(3.D00)*SIDE
NUM=0
DO 260 KEL=1,NBLOS
IF(IPERT(KEL).EQ.0) GO TO 260
NUM=NUM+1
DZ=ZZ(1,IPERT(KEL))
VOL0=TTTT*DZ*FRZ(KEL)
DO 194 K5=0,1
DO 193 K4=0,IELEM-1
DO 192 K3=0,IELEM-1
DO 191 K2=1,IELEM+1
KNW1=KN(NUM,3+K5*NELEH+(K4*IELEM+K3)*(IELEM+1)+K2)
KNX1=KN(NUM,3+(K5+2)*NELEH+(K4*IELEM+K3)*(IELEM+1)+K2)
KNY1=KN(NUM,3+(K5+4)*NELEH+(K4*IELEM+K3)*(IELEM+1)+K2)
INW1=ABS(KNW1)
INX1=ABS(KNX1)-LL4W
INY1=ABS(KNY1)-LL4W-LL4X
DO 190 K1=0,IELEM-1
IF(V(K2,K1+1).EQ.0.0) GO TO 190
IF(K5.EQ.0) THEN
SSS=(-1.0)**K1
JND1=(NUM-1)*IELEM**3+K4*IELEM**2+K3*IELEM+K1+1
JND2=(KN(NUM,1)-1)*IELEM**3+K4*IELEM**2+K3*IELEM+K1+1
JND3=(KN(NUM,2)-1)*IELEM**3+K4*IELEM**2+K3*IELEM+K1+1
ELSE
SSS=1.0
JND1=(KN(NUM,1)-1)*IELEM**3+K4*IELEM**2+K1*IELEM+K3+1
JND2=(KN(NUM,2)-1)*IELEM**3+K4*IELEM**2+K1*IELEM+K3+1
JND3=(KN(NUM,3)-1)*IELEM**3+K4*IELEM**2+K1*IELEM+K3+1
ENDIF
IF(KNW1.NE.0.0) THEN
KK=0
DO 130 I=1,2*IELEM
IF(IPBBW(I,INW1).EQ.JND1) THEN
KK=I
GO TO 140
ENDIF
130 CONTINUE
CALL XABORT('TRICHH: BUG3.')
140 SG=REAL(SIGN(1,KNW1))
BBW(KK,INW1)=BBW(KK,INW1)+SG*SSS*REAL(VOL0/DENOM)*V(K2,K1+1)
ENDIF
IF(KNX1.NE.0.0) THEN
KK=0
DO 150 I=1,2*IELEM
IF(IPBBX(I,INX1).EQ.JND2) THEN
KK=I
GO TO 160
ENDIF
150 CONTINUE
CALL XABORT('TRICHH: BUG4.')
160 SG=REAL(SIGN(1,KNX1))
BBX(KK,INX1)=BBX(KK,INX1)+SG*SSS*REAL(VOL0/DENOM)*V(K2,K1+1)
ENDIF
IF(KNY1.NE.0.0) THEN
KK=0
DO 170 I=1,2*IELEM
IF(IPBBY(I,INY1).EQ.JND3) THEN
KK=I
GO TO 180
ENDIF
170 CONTINUE
CALL XABORT('TRICHH: BUG5.')
180 SG=REAL(SIGN(1,KNY1))
BBY(KK,INY1)=BBY(KK,INY1)+SG*SSS*REAL(VOL0/DENOM)*V(K2,K1+1)
ENDIF
190 CONTINUE
191 CONTINUE
192 CONTINUE
193 CONTINUE
194 CONTINUE
DO 253 K5=0,2 ! THREE LOZENGES PER HEXAGON
DO 252 K2=0,IELEM-1
DO 251 K1=0,IELEM-1
KNZ1=KN(NUM,3+6*NELEH+2*K5*IELEM**2+K2*IELEM+K1+1)
KNZ2=KN(NUM,3+6*NELEH+(2*K5+1)*IELEM**2+K2*IELEM+K1+1)
INZ1=ABS(KNZ1)-LL4W-LL4X-LL4Y
INZ2=ABS(KNZ2)-LL4W-LL4X-LL4Y
DO 250 K3=0,IELEM-1
IF(K5.EQ.0) THEN
JND1=(NUM-1)*IELEM**3+K3*IELEM**2+K2*IELEM+K1+1
ELSE
JND1=(KN(NUM,K5)-1)*IELEM**3+K3*IELEM**2+K2*IELEM+K1+1
ENDIF
IF(KNZ1.NE.0) THEN
KK=0
DO 210 I=1,2*IELEM
IF(IPBBZ(I,INZ1).EQ.JND1) THEN
KK=I
GO TO 220
ENDIF
210 CONTINUE
CALL XABORT('TRICHH: BUG6.')
220 SG=REAL(SIGN(1,KNZ1))
BBZ(KK,INZ1)=BBZ(KK,INZ1)+SG*REAL(VOL0/DZ)*V(1,K3+1)
ENDIF
IF(KNZ2.NE.0) THEN
KK=0
DO 230 I=1,2*IELEM
IF(IPBBZ(I,INZ2).EQ.JND1) THEN
KK=I
GO TO 240
ENDIF
230 CONTINUE
CALL XABORT('TRICHH: BUG7.')
240 SG=REAL(SIGN(1,KNZ2))
BBZ(KK,INZ2)=BBZ(KK,INZ2)+SG*REAL(VOL0/DZ)*V(IELEM+1,K3+1)
ENDIF
250 CONTINUE
251 CONTINUE
252 CONTINUE
253 CONTINUE
260 CONTINUE
RETURN
*
600 FORMAT(/52H TRICHH: MAXIMUM BANDWIDTH FOR W-ORIENTED MATRICES =,
1 I4/27X,25HFOR X-ORIENTED MATRICES =,I4/27X,16HFOR Y-ORIENTED M,
2 9HATRICES =,I4/27X,25HFOR Z-ORIENTED MATRICES =,I4)
610 FORMAT(/40H TRICHH: LENGTH OF W-ORIENTED MATRICES =,I10/16X,
1 24HOF X-ORIENTED MATRICES =,I10/16X,24HOF Y-ORIENTED MATRICES =,
2 I10/16X,24HOF Z-ORIENTED MATRICES =,I10)
END
|
